## Accuracy of the Butterworth Filters

### The Low Pass and High Pass Filter

The order calculating formula given in Mathematics - Prototype in the help menu is very reliable. In over 100 SwitcherCAD tested examples, the attenuation was equal to or greater than the requested attenuation at the stop frequency. For low pass filters, the attenuation increased for all progressively higher frequencies. For high pass filters, the attenuation increased for all progressively lower frequencies. In every case, the 3 dB down frequency was less than 0.5% from the specified frequency. This is likely because of the step function nature of order being imposed on a continuous frequency spectrum. It would be wise to do a simulation for any filter generated by the Butterworth Calculator.

### The Band Pass Filter

Left Side of the Response Curve

The order calculating formula given in Mathematics - Prototype in the help menu is not reliable. Consider the center frequency as marking the center of the filter response function. In all SwitcherCAD tested examples, the attenuation was near the requested attenuation at the stop frequency on the left side of the response function. At lower orders, the estimated order tended to be one order lower than required. At orders above 10, the estimate tended to be one or two orders higher than required. In every observed case, the 3 db down pass band frequency corners were less than 0.5% from the specified frequency on the left side and on the right side of the response curve.

Right Side of the Response Curve

Where the real trouble lies is at the ends of the stop bandwidth on the right side of the response graph. At the requested endpoint of the stop band, the attenuation was less than that requested in all but a few cases at low orders. In almost every case the estimated order was two or more orders less than needed. The conclusion: enter specifications, compute the filter, then do a simulation. If the filter is insufficient, recompute the filter doing a manual order entry, then do the simulation again.

It proved unwise to add one to the order computation because this led to significant order errors for orders less than about six.

The suggestion here is that it may be wise to cascade a low pass and then a high pass filter with different orders to tailor the response curve to fit desired specifications. This will lead to a filter with fewer reactances. Further, it's a good idea because the response curve is not symmetrical about either the arithmetic or the geometric center.

### The Band Stop Filter

The stop band filter has the same problems as given in the band pass filter section. That means the same suggestions are advised.

I tested several dozens of circuits with the SwitcherCad simulator. Via typographcial errors:

## Some Good News

• I discovered that transposing the digits of some of the reactance values caused very small changes in the response curve in most cases. These typing errors ranged from a few percent to more than 50% of the design value.
• I discovered that wiring the circuit incorrectly would cause flat spots or small dips in the response curve. For example I would connect the next parallel resonant circuit to the middle of the series resonant circuit in a band stop filter and find that the circuit still worked surprisingly well.
• I discovered that using two standard value capacitors in parallel to achieve a value close to the design, assuming I would wind inductors within one percent, generated filters that were still on target, if not exactly in the bull's eye.